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41399193=3*11*101*12421; 101 = ((3^4)+(11^2))/2 and 12421 = ((11^4)+(101^2))/2, so 41399193 is a member.

MAPLE

n := 20: L := []: for a from 3 to n do if isprime(a) then for b from a to n^2 do if isprime(b) then c := (a^4+b^2)*(1/2); if isprime(c) then d := (b^4+c^2)*(1/2); if isprime(d) then L := [op(L), a*b*c*d]: end if end if end if end do end if end do; L := sort(L)